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erma4kov [3.2K]
3 years ago
7

Aran moved a cone-shaped pile of sand that had a height of 6 ft and a radius of 3 ft. He used all of the sand to fill a cylindri

cal pit with a radius of 6 ft. How high did the sand reach in the pit? Use 3.14 to approximate pi
Mathematics
1 answer:
VMariaS [17]3 years ago
5 0
Volume of sand = Volume of sand in the cylindrical pi
1/3 πr^2h = πr^2h
1/3 x 3.14 x 3^2 x 6 = 3.14 x 6^2 x h
6h = 3
h = 3/6 = 1/2 ft

The height of the sand in the pit is 0.5 ft.
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Terry and Callie do word processing. For a certain prospectus Callie can prepare it two hours faster than Terry can. If they wor
Dahasolnce [82]

Time taken by jerry alone is 10.1 hours

Time taken by callie alone is 8.1 hours

<u>Solution:</u>

Given:- For a certain prospectus Callie can prepare it two hours faster than Terry can

Let the time taken by Terry be "a" hours

So, the time taken by Callie will be (a-2) hours

Hence, the efficiency of Callie and Terry per hour is \frac{1}{a-2} \text { and } \frac{1}{a} \text { respectively }

If they work together they can do the entire prospectus in five hours

\text {So, } \frac{1}{a-2}+\frac{1}{a}=\frac{1}{5}

On cross-multiplication we get,

\frac{a+(a-2)}{(a-2) \times a}=\frac{1}{5}

\frac{2 a-2}{(a-2) \times a}=\frac{1}{5}

On cross multiplication ,we get

\begin{array}{l}{5 \times(2 a-2)=a \times(a-2)} \\\\ {10 a-10=a^{2}-2 a} \\\\ {a^{2}-2 a-10 a+10=0} \\\\ {a^{2}-12 a+10=0}\end{array}

<em><u>using quadratic formula:-</u></em>

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

x=\frac{12 \pm \sqrt{144-40}}{2}

\begin{array}{l}{x=\frac{12 \pm \sqrt{144-40}}{2}} \\\\ {x=\frac{12 \pm \sqrt{104}}{2}} \\\\ {x=\frac{12 \pm 2 \sqrt{26}}{2}} \\\\ {x=6 \pm \sqrt{26}=6 \pm 5.1} \\\\ {x=10.1 \text { or } x=0.9}\end{array}

If we take a = 0.9, then while calculating time taken by callie = a - 2 we will end up in negative value

Let us take a = 10.1

So time taken by jerry alone = a = 10.1 hours

Time taken by callie alone = a - 2 = 10.1 - 2 = 8.1 hours

3 0
3 years ago
If one of the roots of the quadratice quation x2+kx-12=0is4,what is the value of k?
uysha [10]
<h3>Given Equation:</h3>

\huge \purple {\rm { {x}^{2}  + kx - 12 = 0}}

<h3>Value:</h3>

\huge \purple {\rm {x = 4}}

<h3>To Find:</h3>

\huge \purple {\rm {The \: value \: of \: k.}}

<h3>Solution:</h3>

\huge \purple {\rm { {(4)}^{2}  + k(4) - 12 = 0}}

\huge \purple {\rm {or, \: 16 + 4 k - 12 = 0}}

\huge \purple {\rm {or, \: 4k =  - 4}}

\huge \purple {\rm {or, \: k =  \frac{ - 4}{4}  =  - 1}}

<h2>Answer:</h2>

\huge \purple {\sf {The \: value \: of \: k \: is \: -1}}

3 0
3 years ago
Read 2 more answers
34=−2t can u help me
lys-0071 [83]
34 = -2t....divide both sides by -2
(-34/2) = (-2/-2)t
- 17 = 1t, or just t

so ur answer is : t = -17
3 0
3 years ago
A local park has a grassy playground that is 3/5 mile long and 1/3 mile wide. What part of a square mile does the playground cov
adell [148]

Answer:

The playground covers \frac{1}{5} of a square mile


Step-by-step explanation:

The playground is a rectangular ground. The area of a rectangle is given by legth * width, hence,

The area of the playground is length * width

Area = \frac{3}{5}*\frac{1}{3}=\frac{3}{15}=\frac{1}{5} sq. mi


Hence the playground cover \frac{1}{5} of a square mile

5 0
3 years ago
I need help ASAP!!Please make sure u sure the answer is correct.
Alina [70]

Answer:

(x-8)^2+(y-16)^2 = 4

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2+(y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x-8)^2+(y-16)^2 = 2^2

(x-8)^2+(y-16)^2 = 4

6 0
3 years ago
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